Questions on the circle, a curve composed of points that are at a fixed distance from a fixed point.

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5
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1answer
280 views

Extension of real analytic map on the unit circle

Given a real-analytic map $f : \mathbb{S}^1 \rightarrow \mathbb{S}^1$, where $$\mathbb{S}^1 = \{z \in \mathbb{C} : |z| = 1\},$$ does it admit a complex-analytic extension $\tilde{f} : U \rightarrow ...
1
vote
1answer
108 views

Function to Generate Two Circles For a Color Gradient

I am working on a project creating a gauge package in software, but I am posting here because it is more of a mathematical question. In short, I need a function to create a color gradient to fill in ...
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2answers
873 views

Check if point on circle is in between two other points (Java)

I am struggling with the following question. I'd like to check if a point on a circle is between two other points to check if the point is in the boundary. It is easy to calculate when the boundary ...
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2answers
550 views

How to calculate a specific area inside a circle?

I want to calculate the area displayed in yellow in the following picture: The red square has an area of 1. For any given square, I'm looking for the simplest ...
14
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6answers
11k views

A circle with infinite radius is a line

I am curious about the following diagram: The image implies a circle of infinite radius is a line. Intuitively, I understand this, but I was wondering whether this problem could be stated and ...
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2answers
1k views

Angle of reflection off of a circle?

I've made simple 2D games in the past using mostly just squares. If an object collided with another object (all squares/rectangles) it would just change the slope to the opposite based on what side ...
3
votes
2answers
86 views

every point on boundary of region of convergence is singular

I am given the following function: $$f(z)=1+z^2+z^4+z^8+z^{16}+ \cdots$$ and shall show that it is holomorphic in the unit disc, that $f\to\infty$ as $z\to e^{2i\pi/2^n}$, and that every point on ...
2
votes
1answer
147 views

Intersections of 2 circles

Let me ask a similar question to the one I did yesterday. I got answers which said that the following problem had no general solution for x and y. $\sqrt{(n_1-x)^2+(n_2-y)^2}=n_3$ ...
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votes
4answers
2k views

Is an ellipse a circle transformed by a simple formula?

Does any ellipse $E$ have a circle $C$ such that you can obtain $E$ by transforming $C$ by a simple formula $F$? In details , both $E$ and $C$ have the same center and the axes of $E$ are the XY axes. ...
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2answers
1k views

Find, inside a large circle, the maximum number of small circles placed 60 degrees to each other and

... starts with a small circle in the center of the large circle. The above picture shows a program I wrote to actually draw the circles out. But you can see that this method does not yield maximum ...
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vote
2answers
279 views

how to get the width of a segment of a circle, given its area?

On a circle, 2 parallel chords delimit a segment of which we know the area : A. We also know the distance to the center of the circle of 1 chord : d1. How to find d2, the distance of the other chord ...
5
votes
1answer
315 views

Area of a circle taken as equal to that of a square

I just picked up this book Intro to foundations and fundamental concepts of math (Howard Eves/Carroll Newsom) Practice problem: In the Rhind papyrus area pf a circle is taken as equal to that of a ...
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4answers
1k views

How to equally divide a circle with parallel lines?

How can I "draw" $n$ parallel lines in such a way that they will divide a circle (disc) in $n+1$ equal areas ?
9
votes
7answers
8k views

a circle graph is not a function?

I'm a little confused by the rule: If you draw a vertical line that intersects the graph at more than 1 point then it is not a function. Because then a circle like $y^2 + x^2 = 1$ is not a function? ...
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vote
2answers
131 views

Angles And Their Measurements

I have an intuitive understanding of what degrees and radians are and what arc length, subtending, area of the sector and the derivation of the formula $$s = r \cdot \theta.$$ However due to lack of ...
5
votes
2answers
217 views

Center and radius of circle question

For a circle that has the equation $(x-a)^2 + (y-b)^2 = r^2$ , I know it has center $(a,b)$ and radius $r$. But what happens if the equation is $x^2 + (y-b)^2 = r^2$ ? With $b$ not equal to $0$ and ...
2
votes
1answer
380 views

Concentric circles(IMO 1988/Problem 1)

Let us consider 2 concentric circle radii R and r (R > r) with centre O.We fix P on the small circle and consider the variable chord PA of the small circle. Points B and C lie on the large circle; ...
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2answers
258 views

Finding centre and radius of circle

Let $a,c \in \mathbb R$ with $a \neq 0$, and let $b \in \mathbb C$. Define $$S=\{z\in \mathbb C: az\bar{z}+b\bar{z}+\bar{b}z+c=0\}.$$ a. Show that $S$ is a circle, if $|b|^2 > ac$. ...
11
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5answers
14k views

Parametric Equation of a Circle in 3D Space?

So, my dilemma here is... I have an axis. This axis is given to me in the format of the slope of the axis in the x,y and z axes. I need to come up with a parametric equation of a circle. This circle ...
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vote
2answers
335 views

How can I find an upper bound for the radius of an arc, given arc length and chord length?

This is similar to this question, except I am finding the radius now using the Bisection method and then Newton's method for finding a zero. This is a computer science for a Numerical Methods course. ...
2
votes
2answers
400 views

Calculating point on circle after time

I have a question that seems very similar to calculating-point-around-circumference-of-circle-given-distance-travelled and calculating-point-on-a-circle-given-an-offset, but I don't believe they are ...
1
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1answer
374 views

A plane Geometry Problem

The triangle $ABC$ has $CA=CB$, circumcenter $O$ and incenter $I$. The point $D$ on $BC$ is such that $DO$ is perpendicular $BI$. Show that $DI$ is parallel to $AC$.
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2answers
349 views

Problem on circles- Plane Geometry

The chord CD of a circle center O is perpendicular to the diameter AB. The chord AE goes through the midpoint of the radius OC. Prove that the chord DE goes through the midpoint BC.
0
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1answer
105 views

circle that touch quadrantal internally

I want to know how to construct circle that touch quadrantal(1/4 part of circle) internally. I spend several hours for solving this problem but I have no luck. I attached the picture what I've ...
4
votes
1answer
177 views

Determine if circle is covered by some set of other circles

Suppose you have an existing set of circles $\mathcal{C} = {C_1, .., C_n}$ each with a fixed radius $r$ but varying centre coordinates. Next, you are given a new circle $C_{n+1}$ with the same radius ...
0
votes
1answer
114 views

How do you express how much a curve or part of a circle is “bent”?

Given a certain curve, or part of a circle, how do you express how much it is bent? If I have for example 1/3 of a circle (without seeing the full circle). How do I calculate and express that it is ...
8
votes
2answers
443 views

Coloring a sphere with minimum colors (with constraints)

This is a problem we've been considering in our undergraduate math club, and I thought it would be nice to get further thoughts on the subject. I will start with a two dimensional case and then ...
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2answers
108 views

Is circle formula same in different XY system?

I want to check an element if it's in a circle in my browser. I know the circle formula from my high school: But I'm not sure if it's same in browser XY system too. Because browsers zero ...
1
vote
1answer
1k views

Area of a square using circle

So I have this square and theres a circle inside of it. The circle of radius $r$ is inscribed in the square. So how do I find the area of the square in terms of $r$? I know that area of a circle is ...
0
votes
1answer
161 views

What is the ratio of the area?

If the segment A'B' is tangent to the incircle of triangle ABC, and that segment AB = segment CM; then, what is the ratio of the area of the triangle ABC to the area of the small triangle A'B’C? ...
0
votes
0answers
246 views

A section of the circle's ring

What is the simplest way to calculate the area of the blue section of the circle's ring shown below using the following datas : a) K is the center of the square ABCD, b) Vertices A and C are on the ...
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votes
2answers
166 views

Algorithm to randomly place circles at least $D$ distance away from one another

I'm trying to work out how to write an algorithm to randomly place circles of $R$ radius, in a 2d rectangle of arbitrary dimensions, such that each placed circle is at least $D$ distance away from ...
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0answers
93 views

How to determine the center of a circle with pen and straightedge [duplicate]

Possible Duplicate: Determine the centre of a circle My buddy draws a circle then he erase its center. He quiz me how can find the center with only pen and straightedge (no compass). Do ...
2
votes
3answers
604 views

what formula describes the convex hull of two circles (i.e. two circles connected by tangent lines)?

I'm investigating the following problem. Imagine a circle at the origin with radius r. The circle moves upward with speed s and its radius simultaneously increases by a length of b per time unit. ...
5
votes
1answer
289 views

Is this concept of circle geometry known?

Astonishingly, no mathematician ever could give a "Mr. Foobar invented this" whenever I came up with this construction, although it is very elementary. Given are 3 circles C1,C2,C3 (avoid degenerate ...
4
votes
2answers
331 views

rotating 90 degrees around a circle on a co-ordinate plane

I thought the answer would be square root of 3. It would seem that the x co-ordinate of Q would just be the opposite of the x co-ordinate of P. I'm not sure if the picture is just being ...
2
votes
2answers
413 views

Chord dividing circle , function

Two chords PA and PB divide circle into three parts. The angle PAB is a root of f(x)=0. Find f(x) Clearly , PA and PB divides circle into three parts means it divides it into 3 parts of equal areas ...
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vote
2answers
3k views

Calculating point around circumference of circle given distance travelled

Its the end of the day and my brain just cant cope anymore. Can anyone help with, what I hope, is a simple question.. Given a point on a circle (x, y coordinates) how can I calculate the coordinates ...
2
votes
1answer
92 views

Finding the location of the end of an arc, knowing the beginning, the arc's length and the radius

I apologise in advance if this is really basic. I have a circle of radius 15, from which i work out an arc, given an angle of arbitrary value (it's for a computer program). Given that i know the point ...
3
votes
2answers
273 views

Circle bitangent angles

Say we have two circles $C_1$ and $C_2$ with radii $r_1$ and $r_2$, respectively. Let their centers be $d$ units apart. There are 4 bitangents, two outer and two inner. Examine the intersection of an ...
2
votes
4answers
3k views

line segment joining two centers of circles is perpendicular to line segment joining two intersection point of the circles

Prove that the line segment joining the two centers of the concurrent circles of equal radius is perpendicular to line segment joining the two intersection points of the circles. I had come across ...
3
votes
2answers
955 views

Area Between Three Circles of Differing Radii

From the link in wikipedia http://web.gnowledge.org/wiki/index.php/Area_Between_Three_Circles_of_Differing_Radii OPEN QUESTION: What is the equation, in three variables, relating the radii of ...
6
votes
3answers
2k views

Definite integral: $\displaystyle\int^{4}_0 (16-x^2)^{\frac{3}{2}} dx$

The following integral can be computed using the substitution $x = 4\sin\theta~$ and then proceeding with $dx = 4\cos\theta~ d\theta~$, and evaluating the integral of $\cos^4\theta~$: ...
0
votes
3answers
484 views

Formula for gallons in a trough

I have a trough which is a circular container. How do I determine how many gallons of water it takes to fill up the trough? I was thinking that we measure the height and the width but I think it's a ...
5
votes
1answer
246 views

What is the mathematical principle that describes a series of dots on concentric circles that form a spiral pattern?

Apologies for the vagueness of the question, I'll clean it up once an answer helps me describe it better. I'm fascinated by the pattern demonstrated in this image. It's made up of dots on a series ...
6
votes
4answers
3k views

Can a circle truly exist?

Is a circle more impossible than any other geometrical shape? Is a circle is just an infinitely-sided equilateral parallelogram? Wikipedia says... A circle is a simple shape of Euclidean geometry ...
6
votes
3answers
92 views

Algorithm to determine if a collection of unit discs covers the unit disc centered at the origin?

I have a list of points $ (x_i, y_i) $ for $i = 1...n$. Is there an algorithm to determine if the union of the unit discs centered at these points is a superset of the unit disc centered at $(0, 0)$? ...
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4answers
5k views

How do you find the formula for an area of the circle through integration?

I got this question on my Maths exam today, and the Department of Education has stated it is on the syllabus, but none of the three textbooks I could get my hands mention anything about it. One ...
1
vote
3answers
673 views

Inscribed kissing circles in an isosceles trapezoid

5 equal circles in an isosceles trapezoid. Radius of circle is 4. Find black colored area. I don't have any ideas, could you give me a hand? Thanks.
12
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1answer
223 views

A question on circles

Given that a lamp-post can light a surrounding circle of radius 100 m, what is the minimum number of such lamp-posts required to light a circular ground of radius 1000 m.